Rembrandt’s A Child Being Taught to Walk, c1656

David Hockney: The moment you put down two or three marks on a piece of paper, you get relationships. They’ll start to look like something. If you draw two little lines they might look like two figures or two trees. One was made first, one second. We read all kinds of things into marks. You can suggest landscape, people and faces with extremely little. It all depends on the human ability to see a mark as a depiction.

Martin Gayford: The whole of picture-making is based on our capacity to see one thing as another. We can find such images in the sky, or, as Leonardo da Vinci suggested, on “walls spotted with various stains, or with a mixture of different kinds of stones”. In such random marks, Leonardo, who surely had a powerful imagination, could make out “landscapes adorned with mountains, rivers, rocks, trees, plains, wide valleys, and various groups of hills”.

DH: We obviously want to see pictures, don’t we? We are geared to seeing images on a flat surface. If we put down four marks, everybody knows it could be a face.

MG: That’s part of the alchemy of art, how an artist can transform one thing into another.

Rembrandt’s A Child Being Taught to Walk (c1656). Photograph: The Trustees of the British Museum

DH: The Chinese regarded not acknowledging the brush and the marks it makes as a bit crude; to them, that was trying to cover something up, so not such a high form of art. European art historians don’t look at China very much. But I suspect Rembrandt must have known Chinese drawings, and had probably seen a few. Amsterdam was a port, and the Dutch were trading a great deal in the far east. For example, a Chinese master looking at Rembrandt’s drawing of a family, now in the British Museum, would recognise it as a masterwork.

The child is being held by her mother and older sister. The mother grips the child firmly, the sister more hesitantly, and Rembrandt observes her looking at the child’s face to see how anxious she is. The lines of her shoulders beautifully indicate this; Rembrandt even turned his pen round and scratched through the ink to emphasise it. It makes me see the child’s face, a hint of worry in it, indicated only by one or two faint marks. One then begins to look at ink, not mothers and sisters, and marks made by a hand, speedily.

The trace of Rembrandt’s hand is still alive. Your eye can go back and forth between brown ink: sister; fast mark: mother. How rewarding this is, to move from the physical surface of the paper to its disappearance when you read the “subject”, and then back again. How many marvellous layers does this drawing have?

The mother has a double profile, Picassoesque. Was it an accident with the pen that he then used as a master would? Both profiles are fascinating about her character. Her skirt is a bit ragged, without any real detail; one seems to know this, and then marvels at how these few lines suggest it. Then, there’s a passing milkmaid, perhaps glancing at a very common scene, and we know the milk pail is full. You can sense the weight. Rembrandt perfectly and economically indicates this with – what? Six marks, the ones indicating her outstretched arm. Very few people could get near this. It is a perfect drawing.

Caravaggio’s Judith Beheading Holofernes (1598–99)

DH: I have always noticed shadows simply because there weren’t many in Bradford.

MG: The shadow is a negative phenomenon: it is an area behind an opaque object that is shielded from the source of light. If the illumination comes from a single point then the shadow is sharp-edged. In effect, it is a projected negative image: an area of darkness surrounded by an outline.

DH: The shadow is just the absence of light. But do we necessarily always see shadows? You don’t have to see them consciously. The fact that people can take a photograph with their own shadow in it without noticing suggests that they are not aware of them. You can ignore shadows when you are drawing, as the ancient Greeks did, for example. I can, if I draw with just a line; you can choose not to put them in.

MG: In film noir, strong lighting and its deep shadows create the dramatic atmosphere. Without the shadows, this idiom would be far less effective.

DH: It is a kind of joke, but I really mean it when I say Caravaggio invented Hollywood lighting. It is an invention, in that he quickly worked out how to light things dramatically. I’ve always used shadows a bit, because that’s what you need below a figure to ground it, but mine are more like Giotto’s than Caravaggio’s. I use shadows that you see in ordinary lighting conditions; you don’t find ones like Caravaggio’s in nature.

But there are other varieties of Hollywood lighting. The Mona Lisa is one of the first portraits with very blended shadows. That face is marvellously lit, the shadow under the nose, and that smile. The soft transition from the cheekbone down to underneath the jaw is extraordinary. The way that you move from the light to the dark flesh is achieved with incredibly subtle, graded paint that would have taken a long time to put on. I’ve no idea how he did it. You don’t quite see it in nature, but you certainly do in optical projections. Those unbelievably soft gradations look photographic. That’s what makes it remarkable, and why she has that enigmatic smile. It is a haunting face.

Monet’s Sunset on the Seine in Winter(1880)

DH: We see with memory, so if I know someone well, I see them differently from the way I might if I’ve just met them. And my memory is different from yours; even if we are both standing in the same place, we’re not quite seeing the same thing. Other elements are playing a part; whether you have been in a place before will affect you, and how well you know it.

MG: Time affects pictures in a variety of ways. One important factor is how long it takes to make a painting, which may be a matter of minutes, hours, days, months or years. Certain subjects come with their own time constraints: one of the problems of landscape painting and drawing is that crucial aspects of the scene are extremely transient.

DH: There are some wonderfully free Monet paintings of the ice melting on the Seine at Vétheuil, done in January 1880. They were so free because it was rare for there to be ice on the Seine, so Monet would have had to have gone down to the river then and there to paint it. That would have made him work very fast. The ice might not have lasted even a night once the thaw had begun.

When the sun is setting you know that you’ve only got one hour before the light goes so you work faster. He must have been doing very intense looking, my God. Obviously, not everybody is capable of it. Pictures can make us see things that we might not notice without them. Monet made us see the world a bit more clearly.

You have to be in a place for a little while to know exactly when you need to be there for the best light, what the best angle is, which way to move, things like that. If the sun is in your eyes, everything will be a silhouette. Painting is an art of time and space, or so it seems to me. A big thing in drawing is being able to put a figure in space. And you make space through time.

MG: All pictures are, in one way or another, time machines. That is, they condense the appearance of something – a person, a scene, a sequence – and preserve it. It takes a certain amount of time to make them. And it also takes time to look at them, varying from a second to a lifetime.

DH: The eye is always moving; if it isn’t moving you are dead. The perspective alters according to the way I’m looking, so it’s constantly changing. In real life when you are looking at six people there are a thousand perspectives. I’ve included those multiple angles of vision in paintings of friends in my studio. If a figure is standing near to me, I look across at his head but downwards at his feet. A still picture can have movement in it because the eye moves.

When a human being is looking at a scene the questions are: What do I see first? What do I see second? What do I see third? A photograph sees it all at once – in one click of the lens from a single point of view – but we don’t. And it’s the fact that it takes us time to see it that makes the space.

Renaissance European perspective has a vanishing point, but it does not exist in Japanese and Chinese painting. And a view from sitting still, from a stationary point, is not the way you usually see landscape; you are always moving through it. If you put a vanishing point anywhere, it means you’ve stopped. In a way, you’re hardly there.

St Peter Healing the Sick with His Shadow by Masaccio (1426-7) and The Arnolfini Portrait by Jan van Eyck (1434)

DH: In Giotto’s Ognissanti Madonna, painted around 1310, there’s dark at the side of her nose and the Christ child’s and under their brows and chins. Their features aren’t in real chiaroscuro but there are enough shadows on them for you to feel the mass and the volumes. But the light and shade he used on faces seem a bit crude to us because they aren’t quite optical; that is, they don’t appear the way they would if seen in an image projected by a lens or in a mirror.

Also, in Giotto the people do not look as if they were studied from living models. Their noses are always a bit the same, although the mouths vary. The eyes are different but they are consistently painted in a slightly flat way. Even so, his figures have vivid expressions and personality.

Now look at Masaccio’s painting of the elderly beggar in St Peter Healing the Sick with His Shadow, from his frescoes in the Brancacci chapel, Florence, which date from the mid-1420s – more than a century after the Giotto. Note the way the light from above is hitting his cheekbone: it is dark underneath there and in the hollow of his cheek. The shadows under the forearms, below the jaw and at the top of the ear are very dark. Masaccio’s figure has shadows in absolutely the right places, subtly painted. This is a much more accurate depiction of shadow than Giotto’s: it’s what we would describe as more naturalistic. Indeed, these are the first shadows in Italian art that look like a photograph of a shadow.

MG: Obviously, there has been a revolutionary development in the history of pictures between these two paintings: Giotto’s from the early 14th century and Masaccio’s fresco around 1426. This transformation involved the use of naturalistic shadow, real models and what we call linear or Renaissance perspective. These elements appear altogether as a package in Masaccio’s pictures.

DH: Before he painted the older beggar Masaccio must have looked hard at a real man, a model. This is a depiction of an individual. And the shadows on his face are placed as they would be seen in a camera. There are no faces in Italian or Flemish art before 1420 that look like this, and that implies that the reason for the change was technological. It must have been. I think Masaccio had a mirror or a lens and used it to project images. An optical projection needed shadows; you cannot make one without them. The first optical projection I made in my studio in California was with a concave mirror; when I saw it I realised the light causes the shadows. A photograph requires the same conditions.

MG: Nonetheless, there is a staggering leap in verisimilitude in the works of Masaccio, and also – even more evidently – in those of his Flemish contemporary, Jan van Eyck. It is perhaps the most extraordinary development in the history of pictures, and one for which art historians have had no adequate explanation.

DH: The extraordinary thing about Van Eyck is how he comes out of nowhere, and has somehow worked out how to translate into paint the different kinds of sheen on brocade cloth, glass, wood, different kinds of metal, stone, glass, wax, flesh, and all sorts of diverse shine and reflections, all absolutely perfectly. It’s almost unbelievable, isn’t it, the more you think about it?

Some historians seem to imagine that Van Eyck’s studio would have been like Cézanne’s: the artist’s lonely vigil. It wouldn’t have been like that at all: it would have been more like MGM. There would have been costumes, wigs, armour, chandeliers, models, all kinds of props. You just have to look at the paintings to see that. It isn’t possible to paint like that from imagination. So his workshop must have been close to a Hollywood movie: costumes, lighting, camera, let’s go!

Vermeer’s The Art of Painting (1666‑1668)

DH: Vermeer and other artists using a camera obscura weren’t really looking at the world, they were looking at a flat projection of it and sometimes you see more that way, especially such things as textures on brickwork or in cloth, and patterns in fabrics. When painting the lovely map on the back wall of The Art of Painting, Vermeer picks up every little crease, every little fold. The sharpest things in the painting are the map and the chandelier, and they are the furthest away. The human eye would not see those so clearly at that distance, but they are the kind of thing exaggerated by a camera. That map would be a perfect subject for optical projections because it is flat, but not quite flat – and that’s why we are interested in looking at it. I don’t think Vermeer could have painted the map freehand with such precision and detail.

MG: Vermeer was an artist visibly enthralled by optical devices. His pictures reveal how he loved the heightened detail and texture he could see with the aid of a lens. But he clearly also appreciated the strange transformations, glitches and distortions it produced. In this respect, Vermeer resembles a contemporary artist such as Gerhard Richter (an avowed admirer of his work). Therefore, to deny the Dutch painter used a lens is to misunderstand his achievement, which lay, precisely, in finding the poetry in this new way of seeing the world.

DH: Understanding a tool doesn’t explain the magic of creation. Nothing can. People say leave some mystery, but actually it’s impossible to take it away. Optical devices don’t make marks; they don’t make the painting. No lens could see the whole of Vermeer’s The Art of Painting with everything in focus. No lens could today, no lens ever could; therefore, he had to refocus and put things where he wanted. He had to construct the scene. It’s a fantastic painting. Also, I like the title: The Art of Painting. It’s not called The Craft of Painting – I know it was once called The Artist’s Studio as well – but it is also immensely about the craft.

What is so amazing is the way the figures fit in space. Your eye looks from the girl’s hand on the trumpet to the knob of the map, and there is space there. It’s done through control and modulation of tones and edges, with unbelievable skill. Finding those equivalents in paint is tremendously hard. The softness between the painter’s hair and the map is fantastic.

MG: Vermeer’s people are reticent and withdrawn, with Rembrandt’s you have the impression that you can read their thoughts. Louis Armstrong was once asked who was the better of two trumpeters called Billy and Bobby. He considered the matter, and pronounced, “Bobby, because he’s got more ingredients.”

DH: In a way, Vermeer and Rembrandt are opposites. But Rembrandt is the greater artist, I think, because he’s got more ingredients than Vermeer. Rembrandt put more in the face than anyone else ever has, before or since, because he saw more. And that was not a matter of using a camera. That was to do with his heart. The Chinese say you need three things for paintings: the hand, the eye and the heart. I think that remark is very, very good. Two won’t do. A good eye and heart is not enough, neither is a good hand and eye. It applies to every drawing and painting Rembrandt ever made. His work is a great example of the hand, the eye – and the heart. There is incredible empathy in it.

• This is an edited extract from A History of Pictures: From the Cave to the Computer Screen by David Hockney and Martin Gayford, published by Thames & Hudson at £29.95. To order a copy for £24.56, go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.